Reproduction rate, feeding process, and liebig limitations in cell populations—II

Abstract

A biological system consisting of a population of cells suspended in a liquid substrate is considered. The general problem addressed in the paper is the derivation of the kinetic pattern of population growth as a statistical effect of a very large number of elementary interactions between a single cell and the molecules of nutrient in substrate. Solution of the problem is obtained in the form of equation expressing the population growth ratec as a function of substrate concentration,C _s. The analytical expression derived is applied to a real bacterial population (Escherichi coli) and kinetic patterns are theoretically computed. The major findings, expressed roughly, without nuances, are: (i) the concentration of nutrient at the cell membrane,C _c, can only be equal to either 0 (for theC _s below some threshold valueC ^*) orC _s (forC _s>C ^*); (ii) the Michaelis-Menten-Monod kinetics observed in experiments is an artifact: the pure (not contaminated by foreign factors) dependence ofc onC _s is actually such that the functionc=c(C _s) has practically linear increase whenC _s<C ^*, and is constant,c=c(C ^*)=const, whenC _s>C ^*; (iii) the Liebig principle is strictly fulfilled: up to a feasible accuracy of observation, under no circumstances can population growth be limited (controlled) by more than one substrate component—replacement of a limiting component for another one is an instant event rather than a gradual process.